A hard drive sold as 1 TB shows up as about 931 GB on your computer, and nothing has gone missing. Two different sets of prefixes are being used: decimal prefixes count in powers of 10, binary prefixes in powers of 2. Learn both and convert between them.
Decimal prefixes go up in powers of 10 (steps of 1000): kilo = 103, mega = 106, giga = 109, tera = 1012. Binary prefixes go up in powers of 2 (steps of 1024): kibi = 210, mebi = 220, gibi = 230, tebi = 240. So 1 KiB = 1024 bytes but 1 kB = 1000 bytes. Memory sizes are naturally powers of 2, which is why the binary prefixes exist.
Fig. 1: decimal prefixes multiply by 1000 each step; binary prefixes multiply by 1024
Section 01
Two ladders.
Open the prefixes mode of the lab and compare each decimal unit with its binary partner. Notice how the gap grows as the units get bigger.
Decimal prefix
Symbol
Bytes
Binary prefix
Symbol
Bytes
kilo
kB
103 = 1 000
kibi
KiB
210 = 1 024
mega
MB
106 = 1 000 000
mebi
MiB
220 = 1 048 576
giga
GB
109 = 1 000 000 000
gibi
GiB
230 = 1 073 741 824
tera
TB
1012
tebi
TiB
240 = 1 099 511 627 776
Each step: decimal units are 1000 times the one below; binary units are 1024 times the one below. So 1 GiB = 1024 MiB, and 1 GB = 1000 MB.
Why binary prefixes exist: memory is addressed in binary, so a memory chip holds a power of 2 bytes, such as 230. Calling that "1 GB" would be inaccurate by more than 7%.
The gap grows: 1 KiB is 2.4% bigger than 1 kB, but 1 TiB is about 10% bigger than 1 TB.
Examiner trap
Read the symbol carefully. MB means 106 bytes and MiB means 220 bytes. If a question uses MiB, divide by 1024 at each step, not 1000.
Section 02
Converting units.
To move down a ladder multiply; to move up divide. Never mix the two ladders in one step: convert to bytes first if you need to switch.
Worked example Binary units
How many bytes are there in 4 MiB? How many bits is that?
1 MiB = 220 = 1 048 576 bytes.
4 × 1 048 576 = 4 194 304 bytes.
Each byte is 8 bits: 4 194 304 × 8 = 33 554 432 bits.
Answer: 4 194 304 bytes = 33 554 432 bits
Worked example Switching ladders
A drive is sold as 500 GB. How many GiB will the operating system report?
Convert to bytes using the decimal ladder: 500 GB = 500 × 109 = 500 000 000 000 bytes.
1 GiB = 230 = 1 073 741 824 bytes.
500 000 000 000 ÷ 1 073 741 824 = 465.66...
Answer: about 465.7 GiB
Your turn
How many 2 MiB photos can be stored in exactly 1 GiB?
1 GiB = 1024 MiB, so 1024 ÷ 2 = 512 photos
Stage 1 · Learn
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How many bytes are in 1 KiB?
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In the lab, which is bigger: 1 GB or 1 GiB?
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How many MiB make 1 GiB?
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What does the prefix tera mean?
Section 03
Where each is used.
Both sets of prefixes appear on real devices, which is why the numbers on the box and the numbers on the screen disagree.
Storage manufacturers usually quote hard disk and SSD sizes with decimal prefixes (GB, TB), which give the larger-looking number.
Main memory (RAM) comes in powers of 2, so its size is exactly expressed with binary prefixes: 16 GiB of RAM is 16 × 230 bytes.
Operating systems often calculate in powers of 2 even when they print the label "GB", so a 1 TB drive appears as about 931 "GB" (really 931 GiB).
Data transfer rates such as 100 Mbps use decimal prefixes and bits, not bytes.
Examiner trap
A capital B is bytes and a small b is bits. 100 Mbps is 100 000 000 bits per second, which is 12 500 000 bytes per second.
Stage 2 · Exam
Exam-style questions
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A file is 3 145 728 bytes. What is its size in MiB?
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Which statement about 1 mebibyte is correct?
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A laptop has 8 GiB of RAM. How many bytes is this?
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Why does a drive labelled 2 TB appear smaller when the operating system measures it in TiB?
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